Since the introduction of the relational database model, a lot of efforts have been spent to describe conditions under which data decompositions can be achieved. In the past, these conditions were expressed in terms of dependencies. Here, we encapsulate more recent approaches based on partitioning in a categorical framework in order to obtain a very general context to study views and decomposition that is also applicable to complex-object models. Thereto, we use the categorical notion of presheaf. We argue that our model provides a more fundamental perspective on the concept of object-orientedness which compared to relational theory has developed in a rather ad-hoc manner. In particular, we show that the notion of sheaf yields a characterization for the presence of object-identity.